Chris' advice is where I would start.
Depending on the model of BluRay player it could be easy if you are comfortable with technology and replacing/PC parts, or it could be a little more complex depending on how the player is constructed.
With some players removing the cover might expose the laser lens mechanism (but that isn't always the case, especially with players based around PC type BluRay drives). If you are lucky in that regard then it's just a case of using a cotton bud damped with cleaning fluid, and gently cleaning the lens. If you are unlucky you'll be presented with the top of the drive itself and will have to disconnect the drive from the unit before removing the cover of the drive itself. In that case don't proceed unless you are happy that you have had a good look, and are sure you can reconnect everything up again. It is usually just a case of disconnecting the data and power cables and then taking out some screws to free up the drive. It might help to note down what goes where, and have a little cup to keep the screws in so you don't lose them. Once you've cleaned the lens give it a short while for the cleaning fluid to evaporate before reassembling.
Another couple of things that can cause such problems:
The type of recordable disc used can have an effect, some players are more comfortable with DVD-R/RW discs than DVD+R/RW, while some are the other way round. Some players will happily play -R or +R discs, but not like -RW or +RW discs. If you have access to different types, try them out (although of course, you'll end up with some disc with the same content, but at least you can resuse the re-writeable ones).
Have you finalised the discs on your PC before playing them?. Some players will happily play unfinalised discs, while many will not.
Finally a misaligned laser lens can result in commercial discs playing while recordable ones wont, but this should be a last resort. Basically, next or near the laser lens will be a tiny screw. Turning it very slightly changes the alignment of the lens. Unfortunately this can be a case of trial and error to find the correct setting, as it is a case of giving the screw a tiny turn (about a quarter turn clockwise or anti clockwise), then reassembling the machine and trying again, if that doesn't work, you have to go through the hole process again and again and again.
Personally I'd go through cleaning the lens first, then trying different types of discs as one of those are likely to be the problem.